Finite Math Examples

$[\begin{array}{c} 1 & 0 & 3 & | - 9 | \\ 0 & 1 & 2 & | 9 | \\ 0 & 0 & 0 & | 0 | \end{array}]$

Step 1

Find the reduced row echelon form.

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Step 1.1

The absolute value is the distance between a number and zero. The distance between $- 9$ and $0$ is $9$ .

$[\begin{array}{c} 1 & 0 & 3 & 9 \\ 0 & 1 & 2 & | 9 | \\ 0 & 0 & 0 & | 0 | \end{array}]$

Step 1.2

The absolute value is the distance between a number and zero. The distance between $0$ and $9$ is $9$ .

$[\begin{array}{c} 1 & 0 & 3 & 9 \\ 0 & 1 & 2 & 9 \\ 0 & 0 & 0 & | 0 | \end{array}]$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$[\begin{array}{c} 1 & 0 & 3 & 9 \\ 0 & 1 & 2 & 9 \\ 0 & 0 & 0 & 0 \end{array}]$

Step 2

The pivot positions are the locations with the leading $1$ in each row. The pivot columns are the columns that have a pivot position.

Pivot Positions: $a_{11}$ and $a_{22}$

Pivot Columns: $1$ and $2$